A heat flow for special metrics

作者：Weiss Hartmut; Witt Frederik^*

来源：Advances in Mathematics, 2012, 231(6): 3288-3322.

DOI：10.1016/j.aim.2012.08.007

• G(2)-manifolds
• Geometric evolution equations
• Quasilinear parabolic equations

On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in G(2). We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorphisms to some critical point for any initial condition sufficiently C-infinity-close to a critical point.

• 出版日期2012-12-20